An analytical solution to the one-dimensional solute advection-dispersion equation in multi-layer porous media

• Published in: Transport in porous media Vol. 30; no. 1; pp. 25 - 43
• Main Authors: CHONGXUAN LIU, BALL, W. P, ELLIS, J. H
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 1998; Springer Nature B.V
• Subjects: Advection; Boundary conditions; Contaminants; Dispersion; Earth sciences; Earth, ocean, space; Eigenvalues; Equilibrium flow; Exact sciences and technology; Exact solutions; Hydrogeology; Hydrology. Hydrogeology; Integral transforms; Multilayers; Porous media; Transport; advection; solutes; eigenvalues; transport; steady flow; spatial distribution; Laplace transformations; solution; mathematical methods; mathematical equations; dispersion; boundary conditions; porous media; methodology
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1023/A:1006596904771

An analytical solution to the one-dimensional solute advection-dispersion equation in multi-layer porous media is derived using a generalized integral transform method. The solution was derived under conditions of steady-state flow and arbitrary initial and inlet boundary conditions. The results obtained by this solution agree well with the results obtained by numerically inverting Laplace transform-generated solutions previously published in the literature. The analytical solution presented in this paper provides more flexibility with regard to the inlet conditions. The numerical evaluation of eigenvalues and matrix exponentials required in this solution technique can be accurately and efficiently computed using the sign-count method and eigenvalue evaluation methods commonly available. The illustrative calculations presented herein have shown how an analytical solution can provide insight into contaminant distribution and breakthrough in transport through well defined layered column systems. We also note that the method described here is readily adaptable to two and three-dimensional transport problems.